Geodesic
Multiplication modules over non-commutative rings
Sbornik. Mathematics, Tome 194 (2003) no. 12, pp. 1837-1864 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

It is proved that each submodule of a multiplication module over a regular ring is a multiplicative module. If $A$ is a ring with commutative multiplication of right ideals, then each projective right ideal is a multiplicative module, and a finitely generated $A$-module $M$ is a multiplicative module if and only if all its localizations with respect to maximal right ideals of $A$ are cyclic modules over the corresponding localizations of $A$. In addition, several known results on multiplication modules over commutative rings are extended to modules over not necessarily commutative rings. 
@article{SM_2003_194_12_a3,
     author = {A. A. Tuganbaev},
     title = {Multiplication modules over non-commutative rings},
     journal = {Sbornik. Mathematics},
     pages = {1837--1864},
     year = {2003},
     volume = {194},
     number = {12},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2003_194_12_a3/}
}
TY  - JOUR
AU  - A. A. Tuganbaev
TI  - Multiplication modules over non-commutative rings
JO  - Sbornik. Mathematics
PY  - 2003
SP  - 1837
EP  - 1864
VL  - 194
IS  - 12
UR  - http://geodesic.mathdoc.fr/item/SM_2003_194_12_a3/
LA  - en
ID  - SM_2003_194_12_a3
ER  - 
%0 Journal Article
%A A. A. Tuganbaev
%T Multiplication modules over non-commutative rings
%J Sbornik. Mathematics
%D 2003
%P 1837-1864
%V 194
%N 12
%U http://geodesic.mathdoc.fr/item/SM_2003_194_12_a3/
%G en
%F SM_2003_194_12_a3
A. A. Tuganbaev. Multiplication modules over non-commutative rings. Sbornik. Mathematics, Tome 194 (2003) no. 12, pp. 1837-1864. http://geodesic.mathdoc.fr/item/SM_2003_194_12_a3/

[1] Tuganbaev A. A., Semidistributive modules and rings, Kluwer Acad. Publ., Dordrecht, 1998 | MR | Zbl

[2] Anderson D. D., “Multiplication ideals, multiplication rings and the ring $R(X)$”, Canad. J. Math., 28 (1976), 760–768 | MR | Zbl

[3] Anderson D. D., “Some remarks on multiplication ideals”, Math. Japon., 4:4 (1980), 463–469 | MR

[4] Barnard A., “Multiplication modules”, J. Algebra, 71:1 (1981), 174–178 | DOI | MR | Zbl

[5] Brewer J. W., Rutter E. A., “A note on finitely generated ideals which are locally principal”, Proc. Amer. Math. Soc., 31 (1972), 429–432 | DOI | MR | Zbl

[6] El-Bast Z. A., Smith P. F., “Multiplication modules”, Comm. Algebra, 16:4 (1988), 755–779 | DOI | MR | Zbl

[7] Larsen M. D., McCarthy P. J., Multiplicative theory of ideals, Academic Press, New York, 1971 | MR | Zbl

[8] Low G. M., Smith P. F., “Multiplication modules and ideals”, Comm. Algebra, 18:12 (1990), 4353–4375 | MR | Zbl

[9] Naoum A. G., Al-Alwan F. H., “Dense submodules of multiplication modules”, Comm. Algebra, 24:2 (1996), 413–424 | DOI | MR | Zbl

[10] Naoum A. G., Hasan M. A. K., “The residual of finitely generated multiplication modules”, Arch. Math. (Basel), 46:3 (1986), 225–230 | MR | Zbl

[11] Singh S., Al-Shaniafi Y., “Multiplication modules”, Comm. Algebra, 29:6 (2001), 2597–2609 | DOI | MR | Zbl

[12] Smith P. F., “Some remarks on multiplication modules”, Arch. Math. (Basel), 50:3 (1988), 223–235 | MR | Zbl

[13] Smith P. F., “Multiplication modules and projective modules”, Period. Math. Hungar., 29:2 (1994), 163–168 | DOI | MR | Zbl

[14] Smith W. W., “Projective ideals of finite type”, Canad. J. Math., 21 (1969), 1057–1061 | MR | Zbl

[15] Tuganbaev A. A., Distributive modules and related topics, Gordon and Breach, Amsterdam, 1999 | MR | Zbl

[16] Tuganbaev A. A., “Stroenie distributivnykh kolets”, Matem. sb., 193:5 (2002), 113–128 | MR | Zbl

[17] Anderson D. D., “Some remarks on multiplication ideals. II”, Comm. Algebra, 28:5 (2000), 2577–2583 | DOI | MR | Zbl

[18] Stenström B., Rings of quotients: an introduction to methods of ring theory, Springer-Verlag, Berlin, 1975 | MR | Zbl

[19] Camillo V. P., “Modules whose quotients have finite Goldie dimension”, Pacific J. Math., 69:5 (1977), 337–338 | MR | Zbl

[20] Kaplansky I., “Projective modules”, Ann. of Math. (2), 68 (1958), 372–377 | DOI | MR | Zbl